S6 Kurtosis

The Kurtosis is the fourth standardized moment -- that is, the fourth raw moment after standardization. This has a natural interpretation as 1 plus the Variance of the Square of the standardized variable. Many other interpretations are given in terms of sharp peaks, and in terms of heavy tails. These are often wrong. However, after standardization, values above 1 SE get raised to the fourth power and quickly become large. Values below 1 SD become very small upon being raised to the fourth power. So the Kurtosis measure the portion of the mass of the random variable lying above 1 SE, and also is heavily influence by the extreme values, or the outliers, in the distribution -- since fourth powers increase very quickly. The technical description is given below

We have seen that the Kurtosis of the standard Normal random variable is 3. In some theoretical contexts, it is the difference from the normal distribution that is important. For this purpose, we define the concept of EXCESS Kurtosis (EK), which is just Kurtosis minus 3. This means that EK of a standard normal is 0. Distributions with Kurtosis greater than 3 have positive Excess Kurtosis and are called leptokurtic. Distributions with Kurtosis less than 3 have negative Excess Kurtosis and are called platykurtic.

Wikipedia: Kurtosis — Article provides the calculations above, and further details on Kurtosis.